Wnil-Injective Modules

A right module M is called Wnil-injective if for any 0 a N( R ), there exists a positive integer n such that an 0 and any right R-homomorphism f : anR M can be extended to R M. In this paper , we first give and develope various properties of right Wnil-injective rings, by which, many of the known results are extended. Also, we study the relations between such rings and reduced rings by adding some types of rings, such as SRB-rings, and other types of rings.